Diffusion Creep of the Lower Mantle and Its Strain Dependence

A recent experimental study (Girard et al., 2016) demonstrated that the Fp (ferropericlase) is substantially weaker than Br (bridgmanite): a volumetrically smaller phase (Fp, ~20 %) is much weaker than a volumetrically major phase (Br, ~60-70 %). Deformation of such two-phase mixture often leads to shear localization in which a large fraction of strain is accommodated by the deformation of Fp. If this is the case in the lower mantle, then deformation in the lower mantle would be localized, and a majority of the lower mantle would not be much deformed. This would have an important implication for the preservation of geochemical heterogeneity in the lower mantle.

To explore this, we started a systematic theoretical study to investigate the nature of the deformation of a two-phase mixture. We focused on two issues. (i) When the two-phase mixture deforms, stress and strain are partitioned in these phases, and the local (internal) stress/strain is no longer the same as the macroscopic stress/strain. (ii) When deformation takes place by diffusion creep, resistance for the deformation depends on grain's shape (strain) as its stress gradient changes with the grain's shape. Hence, the strain localization might be limited in the case of diffusion creep.

To investigate the origin of internal stress, we applied the Eshelby's theory of deformation of an inclusion surrounded by an elastic material (a theory of elasticity can be translated to that of viscous deformation). Using this theory, we studied the stress, strain rate, and vorticity states in a 2D elliptic Fp (weak) grain when it is embedded in Br (strong) matrix subjected to a far-field simple shear. From these mechanical states, the lattice diffusion within Fp grain and its influences on the rheology were investigated using the Finite Element Method. This approach provided important results: (i) average creep rate decreases as the ellipse elongates although the local creep rates are high at the tips of the elongated ellipse. Consequently, (ii) the average viscosity of diffusion creep within Fp grain increases with the straining. These results imply that the strain localization may be restricted in a small range of strain or less when the diffusion is solely considered. Also, the studies of lower mantle dynamics need to consider the strain and geometry dependences of Fp's grain.